**Mechanical Energy Formula**

Mechanical energy is the sum of kinetic energy and potential energy in an object that is used to do a particular work. In other words, it describes the energy of an object because of its motion or position, or both. Â Potential energy is possessed by the object’s position whereas kinetic energy is possessed by the movement. When an object is moving, its potential energy is zero. When itâ€™s at rest, the kinetic energy is zero.

The mechanical energy formula is given by,

**M.E = K. E + P.E**

**M.E = Â½ mv****2**** + mgh**

Where,

**m **= mass of an object,

**v **= velocity of that object,

**g **= acceleration due to gravity and

**h **Â = Â height of an object.

**Example 1**

A person is sitting on a building of height 10m and the mass of the person is 50kg, determine the mechanical energy.

**Solution:**

Given parameters are,

m = 50 kg

h = 10m

the person is not moving, therefore, K. E = 0

Mechanical energy formula is given by,

- E = 1 / 2mv2 + mgh

Since K.E is 0, the equation becomes,

M.E = mgh

Â Â Â = 50 Ã—9.81 Ã—10

Â Â Â = 4905 J

**Example 2**

Determine the mechanical energy of a 20 kg object which is moving with a speed of 10m/s.

**Solution:**

Given parameters are,

m = 20kg

v = 10m/s

the person is moving, therefore P. E = 0

Mechanical energy formula is given by

- E = 1 / 2 mv2 + mgh

Since P.E is 0, the equation becomes,

M.E = 1 / 2mv2

= 1 / 2 Ã— 20 Ã—102

= 1000 J